John,
I know this may be arbitrary, but I have used "type" to mean the logical
concept (same as yours) and "class" to be the OO concept which also embodies an
instance factory. Saying the extent of the type is the class seems contrary to
common usage, at least in OO land.
-Cory (01)> -----Original Message-----
> From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto:ontology-summit-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: Thursday, May 10, 2012 2:03 AM
> To: ontology-summit@xxxxxxxxxxxxxxxx
> Subject: Re: [ontology-summit] First Model Bench Challenge
>
> Dear Matthew and Doug,
>
> MW
> > I do not know what distinction you [JR] make between class and type. I
> > make none.
>
> I sympathize. I would prefer not to use the word 'class' because it has been
> used in so many different ways that any use is an open invitation to
> confusion. In any case, my preferred definition determines a one-to-one
> association between classes and types:
>
> A class is the set of all x of a given type, where type is
> defined by a monadic predicate.
>
> DF
> > You define a class as "the set of all instances of a given type". In
> > order for a definition of a set to identify a timeless group of
> > things, the definition must yield the same group no matter when its
> > extent is calculated.
>
> That is why I prefer to avoid the word 'class'. The O-O people wanted to
>apply
> set-like operators to collections that change their membership in different
> contexts. The word 'type' defined by a monadic predicate has that property.
> You can talk about subtypes and instances in the same way that you can talk
> about sets and members, but the instances can change in different contexts.
>
> MW
> > The spatio-temporal extents [in a 4D view] are considered to exist
> > simpliciter independent of time. You can of course also have the class
> > "Persons alive at 2012-05-08 21:52:00".
>
> I'm happy with that way of talking. But I would prefer to use the word 'set'
> when I focus on the instances and 'type' when I focus on the membership
> criteria. There is never a case when the word 'class' is useful -- except
>when
> talking about notations that use that word.
>
> John
>
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